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Deep Dive into the Math Shifts Understanding Focus and Coherence in the Common Core State Standards for Mathematics The Three Shifts in Mathematics •Focus: Strongly where the standards focus •Coherence: Think across grades and link to major topics within grades •Rigor: Require conceptual understanding, fluency, and application Engaging with the K-2 Content • How would you summarize the major work of K-2? • What would you have expected to be a part of the major work that is not? • Give an example of how you would approach something differently in your teaching if you thought of it as supporting the major work, instead of being a separate, discrete topic. Engaging with the 3-5 Content • How would you summarize the major work of 3-5? • What would you have expected to be a part of the major work? • Give an example of how you would approach something differently in your teaching if you thought of it as supporting the major work, instead of being a separate discrete topic. Coherence Across and Within Grades • It’s about math making sense. • The power and elegance of math comes out through carefully laid progressions and connections within grades. Taken from the Grade 4 Math Course Description on C-Palms website: Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters. Looking For Coherence Within Grades • Examples: 1st grade – 5th grade: Represent and Interpret Data 3rd grade & 5th grade: “Relate area (volume) to multiplication and to addition.” Coherence Within A Grade Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.5 20 Coherence Within A Grade Make a line plot to display a data set of 1 1 1 measurements in fractions of a unit ( 2, 4, 8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 4.MD.4 21 Looking for Coherence Across Grades • Coherence is an important design element of the standards. • “The Standards are not so much built from topics as they are woven out of progressions.” Coherence Card Activity Activity: Place the standards of each theme under the appropriate grade or course. – Separate the cards by theme. – No grade has two of the same theme. – Some “themes” that have only a few cards might represent consecutive grades and some may not. – Read each card in it’s entirety to help determine placement. – Do not check your Standards until you and your colleagues agree on the final product. – Discuss horizontal and vertical observations with your partners. 23 Engaging with the Content • Review your work on Coherence. • Revisit the major focus of each grade/course • Which standards in your progressions are part of the major work, the supporting work, or additional work? Mark them appropriately on your posters using green, blue, or yellow makers. • Discuss the connection between focus and coherence and how the two work in tandem to influence instruction Next Month....... • Your school has been provided with an electronic file containing the 2013-2014 math course descriptions • Next month we will delve even deeper into the CCSS course content Resources: • Common Core Progressions http://ime.math.arizona.edu/progressions/ • PARCC Content Frameworks http://www.parcconline.org/sites/parcc/files/PARCC MCFMathematics_August%202012rev2_FINAL.pdf • Standards Map http://www.cpalms.org/cpalms/unpack_map.aspx • Flip Charts http://katm.org/wp/common-core/